Designing method of optical system

ABSTRACT

An evaluation of an optical system with respect to visual acuity is appropriately performed, with a chromatic aberration of magnification of the optical system being taken into consideration. A performance of the optical system is evaluated based on a correlation between a visual acuity when looking through the optical system and the chromatic aberration of magnification of the optical system, the correlation being a proportional relation such that, when the visual acuity is expressed by a logarithmic visual acuity, the logarithmic visual acuity deteriorates substantially in proportion to the chromatic aberration of magnification, or on a correlation between the visual acuity and an optical value regarding the chromatic aberration of magnification which is substantially equivalent to the correlation.

TECHNICAL FIELD

The present invention relates to a performance evaluation method of anoptical system such as a lens or the like, a designing method of anoptical system using the evaluation method, and an optical systemmanufactured by the designing method.

BACKGROUND ART

For designing a spectacle lens, it is performed to obtain by calculationa lens form which makes its optical performance as optimum as possible,within a range which satisfies a previously determined specification ofthe spectacle lens. As the specification of the spectacle lens,constraint conditions regarding the material, the prescription, or thelike of the lens are given. In the case of a positive lens, a constraintcondition on the center thickness of the lens is given as a furtheradditional specification. Then, the designing of the spectacle lens iscarried out while evaluating the optical performance of the lens using apredetermined function. Such a function is referred to as an evaluationfunction.

Specifically, a parameter which defines the spectacle lens iscategorized in advance into a fixed parameter and a variable parameter.The fixed parameter is a constraint condition. Main items related to theoptical lens design include a lens physicality/form factor (refractivepower, Abbe number, specific gravity, lens surface form data, and thelike), a prescription and fitting state related factor (lens diopter,astigmatic axis, addition, prism, base position, decentration, outsidediameter, far vision PD, near vision PD, lens thickness, VR value (CRvalue+VC value)), an optical factor (diopter data of near vision, farvision, and the like) and other edging specific data. There may also bea case in which frame data (form, DBL, FPD, frame curve, and the like),a frame forward tilt angle, a bevel type and the like are added todesign the lens. Then, first, a ray tracing method, a wave front tracingmethod or the like is used to set plural evaluation points havingdifferent lengths from an optical axis on a refractive surface of thespectacle lens. Next, while changing the value of the variable parameterby predetermined steps, a virtual spectacle lens, which is defined by avalue of the variable parameter at this moment and a value of the fixedparameter, is assumed in each step.

Then, an evaluation value of the whole lens is obtained from values ofthe evaluation function at respective evaluation points of the virtualspectacle lens. Note that a function which defines an evaluation valueof the whole lens using values of an evaluation function at respectiveevaluation points is referred to as a merit function. Then, the value ofthe variable parameter in a step in which the evaluation value becomesan optimum value is specified. In a preferable case, the merit functionbecomes an extremal value within a range which satisfies aspecification. Accordingly, all the parameters which define thespectacle lens are obtained, and the lens is specified as a result.

A calculation which specifies the optimum value of the variableparameter as described above is referred to as an optimizationcalculation. At this time, it is preferred to use a method such as adamped least square method or the like. According to this method, thevalue of the variable parameter is efficiently specified by the leastcalculation amount. Such a calculation method is referred to as a leastcalculation. (For example, International Publication WO 00/62116,Japanese Examined Patent Publication No. Hei 02-38930, or the like.)

The inventor found the following problems in prior arts. Specifically,conventional evaluation functions (merit functions) are intended toevaluate optical performance of a spectacle lens by an aberration amountor the like of the lens itself. However, since the spectacle lens isessentially for visual acuity correction, the degree of deterioration ofthe visual acuity due to the aberration is more important than theaberration amount itself. It is thus preferable to implement not asimple evaluation function, but a kind of an evaluation function withrespect to the visual acuity, namely, a function which prescribes arelation between the visual acuity while looking through an opticalsystem and the aberration or the like of the optical system.Hereinafter, such a function is particularly referred to as a “visualacuity function.” Regarding the relation between the visual acuity andthe aberration, a prior art 1 (Sloan, Louise, “Measurement of visualacuity: a critical review, A. M. A. Arch. Ophthal” (45(6): 704-725,1951)) is known. In this document, an equation I is given as a visualacuity deteriorating part of a minimum separation threshold.2.8[sphere error+0.8(cyl error)]  equation I

In this equation I, it is defined that the sphere error=min (|T|, |S|),the cyl error=∥T|−|S∥, where T is a tangential error, and S is asagittal error.

However, in this document, there are three problems as follows.

-   1. It does not refer to the chromatic aberration.-   2. It does not refer to an eyeball motion (Listing's Law) of an    astigmatic eye.-   3. The “sphere error” and the “cyl error” are measured separately,    but a visual acuity deterioration due to an interrelation between    the “sphere error” and the “cyl error” is not measured.

Therefore, visual acuity deterioration data in which the “sphere error”and the “cyl error” are combined are unreliable, and a tentative theoryof presumption is unconvincing.

Further, in Japanese Patent Laid-open No. Sho 58-24112, the followingdefinition of a visual acuity V is disclosed.V=2^(−2·ĀR−ĀS)   equation VI

Here, ΔR and ΔS are synonyms of the “sphere error” and the “cyl error”respectively in the equation I in the above-described prior art 1.Specifically, they are defined as ΔR=min (|S|, |T|), and ΔS=∥S|−|T∥.

In this publication, similarly to the above-described prior art 1, thereis no reference to the chromatic aberration and the eyeball motion of anastigmatic eye. Further, it does not disclose any theory or reason(measured data or the like) as a basis to derive the equation of thevisual acuity V, so that it is theoretically unreliable and unpractical.

Thus, it is a difficult problem to faithfully express the visual acuityusing the aberration or the like. In other words, when it is tried tofaithfully express the visual acuity, other biophenomena such as theeyeball motion and the like should be taken into consideration.

Further, among various kinds of aberrations, especially a relationbetween the chromatic aberration and the visual acuity is notascertained yet.

For example, in Japanese Examined Patent Publication No. Sho 42-9416, apart of the above described equation I is defined as a Blur Index, andthe “sphere error” and the “cyl error” to which the chromatic aberrationis added are respectively defined as follows. Further, the relation ofthe Blue Index with fraction visual acuity V is shown by the followingequation II to equation V.Blur Index=sphere error+0.8 (cyl error)   equation II

$\begin{matrix}{{{sphere}\mspace{14mu}{error}} = {\frac{{T} + {C} + {S}}{2} - \frac{{T} + {C} - {S}}{2}}} & {{equation}\mspace{14mu}{III}}\end{matrix}$cyl error=∥T|+|C|−|S∥  equation IV

$\begin{matrix}{V = \frac{20}{20 + {56 \times {Blur}\mspace{14mu}{Index}}}} & {{equation}\mspace{14mu} V}\end{matrix}$

Here, C is a chromatic aberration of magnification (transverse chromaticaberration), and is a value obtained by dividing a prism diopter of adeviation angle of a ray which penetrates a lens by an Abbe number.However, in this description, the tangential error is a function ofpupil diameter, and although the chromatic aberration of magnificationis mentioned to be irrelevant to this pupil diameter and the unit isactually different, the tangential error and the chromatic aberration ofmagnification are treated equally. In other words, one diopter of thetangential error and one prism diopter of the chromatic aberration ofmagnification are treated as equal amount of information, which areconsidered to respectively cause an equal amount of the deterioration ofvisual acuity.

This tentative theory has no reason based on any scientific data andcannot be verified, and the conclusion therein is also unconvincing.Further, it does not mention about consideration of the eyeball motion(Listing's Law) in calculation of an astigmatic diopter error.

Therefore, it is unusable for progressive lenses, atoric lenses or thelike.

On the other hand, it is well known that the chromatic aberration ispreferred to be small for visual acuity, and there is a few scientificstudy examples of an effect of the chromatic aberration on visualperformance. Refer to “Kazuhiko Ukai, Hitoshi Ozu, Kaoru Nakajima, OsamuShindo: Megane renzu no shikishuusa to shikinou ni oyobosu eikyou (theeffects of spectacle lenses on chromatic aberration and visualperformance) (KOHGAKU (Optics), 7(1): 21-28, 1977),” (hereinafterreferred to as document 1).

However, the present situation is that, as described above, the relationof the both is not clearly understood to such a degree that at least itcan be applied to designing of an actual optical system. In addition, itis considerable to ignore the chromatic aberration for simplificationand define the visual acuity function with a focus only on aberrationsother than the chromatic aberration. However, since it cannot be clearlysaid that there is no causal relation between the chromatic aberrationand the visual acuity deterioration, it is hard to say that the visualacuity function ignoring the chromatic aberration is accurate.

Incidentally, the chromatic aberration has been ignored in optimizationcalculation in designing spectacle lenses. In other words, amongconventional simple evaluation functions which are not the visual acuityfunction, there is no evaluation function which handles the chromaticaberration substantially as a variable parameter. It is conceivable,first, to be caused by that a selection range of an Abbe number which isclosely correlated to the chromatic aberration is limited from thebeginning to a certain degree in relation to the materials.Specifically, the degree of freedom of the Abbe number is smaller ascompared to degrees of freedom of other factors. Therefore, in designingof optical systems, the Abbe number is not a variable parameter, but isfixed as a constraint condition (specification).

Also it is conceivable, second, to be caused by a recognition thatimaging characteristics of a white light and a monochromatic light in aneyeball optical system are barely different. For more details aboutthis, refer to the following document: “G. A. Fry: Progress in Optics,Vol VIII, p112, ed. by E. Wolf, North-Holland Publishing Company,Amsterdam 1970” (hereinafter referred to as document 2), “KrausKopf J.:J. Opt. Soc. Amer., 52, 1046-1050 (1962) (hereinafter referred to asdocument 3), and “KrausKopf J.: J. Opt. Soc. Amer., 54, 715-716 (1964)(hereinafter referred to as document 4).”

This fact suggests at the same time that even if the Abbe number issacrificed to a certain extent, a lens having a light weight and a goodappearance which is made of a material having a high refractive powercan increase the customer satisfaction more.

However, in the study of the inventor, it is proved that the evaluationor the design of optical systems based only on aberrations other thanthe chromatic aberration of magnification is entirely insufficient.

An object of the present invention is to provide a technique to properlyperform evaluation of an optical system with respect to visual acuity inlight of the chromatic aberration of magnification of the opticalsystem. A further object of the present invention is to provide atechnique to properly design an optical system in light of the chromaticaberration of magnification of the optical system.

DISCLOSURE OF THE INVENTION

According to a first aspect of the present invention, a performanceevaluation method of an optical system is provided, which comprises anoptical performance evaluation step for evaluating a performance of theoptical system based on a correlation between a visual acuity whenlooking through the optical system and a chromatic aberration ofmagnification of the optical system, the correlation being aproportional relation such that, when the visual acuity is expressed bya logarithmic visual acuity, the logarithmic visual acuity deterioratessubstantially in proportion to the chromatic aberration ofmagnification, or on a correlation between the visual acuity and anoptical value regarding the chromatic aberration of magnification whichis substantially equivalent to the correlation.

The logarithmic visual acuity mentioned here refers particularly to,among expression types of visual acuity, a type of visual acuity whichis represented by logarithms. The logarithmic visual acuity includes thefollowing for example:logarithmic visual acuity of logMAR unit=log₁₀ (1/V)logarithmic visual acuity of Nakagawa type=50×log₁₀ V+100logarithmic visual acuity of AGO unit=4×log₂2¹⁰ V

Here, V is the inverse number of a minimum angular resolution (MAR)which is a minimum visual angle capable of recognizing two points or twolines. In addition, the inverse number V of the minimum angularresolution is equivalent to decimal visual acuity, fraction visualacuity, or the like. Hereinafter, the logarithmic visual acuity inlogMAR unit is referred to as “logMAR visual acuity.”

The correlation refers to a correlation between the visual acuity as aconcept including the logarithmic visual acuity, the decimal visualacuity, and the like and the chromatic aberration of magnification, andthus it is not particularly limited to the substantially proportionalrelation between the logarithmic visual acuity and the chromaticaberration of magnification. Therefore, it includes all correlationswhich are substantially equivalent to such a substantially proportionalrelation.

For example, a conversion of the substantially proportional relationbetween the logMAR visual acuity (=log₁₀ (1/V)) and the chromaticaberration of magnification into a correlation between the decimalvisual acuity V and the chromatic aberration of magnification providesthe following result. Specifically, since the deterioration of thelogMAR visual acuity indicates the increase of its value:log₁₀ (1/V)∞ chromatic aberration of magnification this relation isexpressed for convenience as:log₁₀ (1/V)=β×chromatic aberration of magnification then it becomes:log₁₀ V=−(β×chromatic aberration of magnification) therefore:V=10^(−(β×chromatic aberration of magnification))In other words, the decimal visual acuity V deteriorates (decreases)exponentially with the increase of the chromatic aberration ofmagnification. Such an exponential relation is also substantiallyequivalent to the above-described proportional relation.

Further, the optical value regarding the chromatic aberration ofmagnification includes, for example, an Abbe number of the opticalsystem, a prism diopter, and the like.

According to a second aspect of the present invention, a performanceevaluation method of an optical system is provided, which comprises anoptical performance evaluation step for evaluating a performance of theoptical system based on a combination principle, the combinationprinciple of both a first deterioration amount and a seconddeterioration amount when expressing a total deterioration amount due toaberrations of a visual acuity in an optical system when looking throughthe optical system, using the first deterioration amount only due to anaberration other than a chromatic aberration of magnification among theaberrations and the second deterioration amount only due to thechromatic aberration of magnification among the aberrations, thecombination principle in which, when the visual acuity is expressed by alogarithmic visual acuity, the total deterioration amount of thelogarithmic visual acuity becomes a sum of the first deteriorationamount and the second deterioration amount.

Here, the combination principle refers to a combination principle forexpressing the total deterioration amount due to aberrations of visualacuity which is a concept including the logarithmic visual acuity, thedecimal visual acuity, and the like, using the first deteriorationamount and the second deterioration amount, and thus it is notparticularly limited to the relation of the sum when expressing by thelogarithmic visual acuity.

For example, a conversion of the combination principle expressed bylogMAR visual acuity (=log₁₀ (1/V)) into the combination principleexpressed by decimal visual acuity V provides the following result.Specifically, the deterioration of the logMAR visual acuity indicatesthe increase of its value, so that it is expressed for convenience asfollows:log₁₀(1/V)=first deterioration amount+second deterioration amount thenit becomes:log₁₀ V=−(first deterioration amount+second deterioration amount)therefore, the combination principle becomes:V=10^(−(first deterioration amount+second deterioration amount))V=10^(−first deterioration amount)×10^(−second deterioration amount)Such a combination principle is also substantially equivalent to theabove-described relation of the sum.

In addition, the optical system according to the present inventionrefers to an optical system intervening between the crystalline lens ofan eye and a visual object. In other words, it refers to all opticalsystems which are coherently coupled to the crystalline lens of an eye.Such an optical system includes, for example, spectacle lenses, contactlenses, intraocular lenses, head mount displays (HMDs), telescopes,binoculars, microscopes, and the like.

According to a third aspect of the present invention, a performanceevaluation method of an optical system is provided, in which, in theoptical performance evaluation step in the second aspect, theperformance of the optical system is evaluated using a visual acuityfunction which is composed to define a value of the visual acuity fromthe total deterioration amount of the visual acuity by combining a firstterm for obtaining the first deterioration amount and a second term forobtaining the second deterioration amount in accordance with thecombination principle.

Here, the first term is preferred to be composed including a parameterexpressing a power error (also referred to as a curvature of field or amean power error), and a parameter representing an astigmatism or aresidual astigmatism.

Preferably, the first term is composed, when the optical system isformed of a spherical lens, including the parameter expressing the powererror and the parameter expressing the astigmatism, and the first termis composed, when the optical system is formed of an aspherical lens,including the parameter expressing the power error and the parameterexpressing the residual astigmatism.

Here, the residual astigmatism refers to a sum of the astigmatism in acoordinate system of an eyeball which performed a cycloduction based onthe Listing's law, and the astigmatism generated by the optical system.

The reason for selecting the power error and the astigmatism or theresidual astigmatism as the aberration other than the chromaticaberration of magnification is, first, these aberrations affects visualacuity even when a pupil diameter is small. Second, a good visual acuityis provided by approximately two degree including the fovea on a retina.Third, since a good visual acuity is in the vicinity of an optical axisdue to a Stiles-Crawford effect or the like, a spherical aberration anda coma aberration do not largely affect the visual acuity.

Any of these three reasons suggest the existence, in the visual acuity,of a visual system which counterbalances the spherical aberration ofnarrow definition which affects the pupil diameter, and an axialchromatic aberration. Refer to “Mitsuo Ikeda: Shikaku no shinributsurigaku (Psychophysics of Vision) (Morikita Shuppan, 1975),”(hereinafter referred to as document 5), and “Mitsuo Ikeda: Shikisaikohgaku no kiso (Fundamentals of Color Optics) (Asakura Shoten, 1980),”(hereinafter referred to as document 6).

[Relation Between the Chromatic Aberration and the Visual Acuity]

As a result of dedicated studies, the inventor has found first thatthere is a substantially linear relation between a logMAR visual acuitywhen looking through an optical system and the chromatic aberration ofmagnification of the optical system. It will be explained in detailbelow.

The chromatic aberration includes the axial chromatic aberration and thechromatic aberration of magnification. Between them, it has beenreported that the axial chromatic aberration does not affect visualacuity. Refer to the above-described document 1 and “Kazuhiko Ukai:Iroshuusa to megane (Chromatic Aberrations and Spectacles) (Megane nokagaku (Science of Spectacles), vol. 2, 23-49, 1978),” (hereinafterreferred to as document 7).

Accordingly, the inventor studied the relation between the chromaticaberration of magnification and the visual acuity. Unfortunately, thereis no good measurement example of visual acuity deterioration under acondition that the visual acuity is only affected by the chromaticaberration of magnification. Consequently, the following experiment isperformed, and the relation between the chromatic aberration ofmagnification and the visual acuity deterioration is studied based onthe obtained data from the experiment. The condition of the experimentis shown in FIG. 1. The experiment method is as follows.

-   -   (a) A subject is set down on a chair, and an international type        visual acuity chart 1 is placed at 5 [m] apart therefrom. Then,        visual acuity of the subject is measured by the subjective        refraction of fogging method. However, the brightness of the        room is adjusted to 500 [1×].    -   (b) Concretely, each of 7 subjects are measured of their naked        eye vision of left and right eyes separately. Further, visual        acuity of both eyes are measured by subjective refraction.    -   (c) Next, corrected vision of left and right eyes are separately        measured by the similar subjective refraction, and the corrected        vision of both eyes are measured until the maximum value of        being capable to see.    -   (d) Next, as a prism 2, four groups of five types of prisms        respectively having prism values of 10^(Δ), 8^(Δ), 6^(Δ), 4^(Δ),        2^(Δ) are prepared, each of the groups having a different Abbe        number. Then, these prisms are placed in front of a spectacle        lens 3 in turn from the one having the largest diopter to        measure the visual acuity. A trial frame is used for the        placement of the prism 2.

Refractive indexes and the Abbe numbers of the prisms used for thisexperiment are shown in Table 1.

TABLE 1 Refractive indexes (d line) Abbe number (d line) 1.806 40.91.702 40.2 1.523 59.2 1.700 31.0

Further, the naked eye vision, the corrected vision, and theexperimented visual acuity measurement values of each of the sevensubjects (denoted by No. 1 to No. 7) are respectively shown in Table 2to Table 8. In the tables, R denotes a right eye, L denotes a left eye,and B denotes both eyes.

TABLE 2 No. 1 27 years old Male R L B Naked eye vision 0.9 0.7 1.0Corrected vision 1.0 1.0 1.2 ν_(d) = 59.2 ν_(d) = 40.9 ν_(d) = 40.2ν_(d) = 31.0 2^(Δ) 1.2 1.0 p 1.0 p 1.0 p 4^(Δ) 1.0 p 1.0 p 1.0 p 1.0 p6^(Δ) 1.0 p 1.0 p 1.0 p 1.0 8^(Δ) 1.0 1.0 1.0 0.9 10^(Δ)  1.0 0.9 0.9 p0.7 p

TABLE 3 No. 2 24 years old Male R L B Naked eye vision 2.0 1.2 2.0Corrected vision 1.5 1.5 2.0 ν_(d) = 59.2 ν_(d) = 40.9 ν_(d) = 40.2ν_(d) = 31.0 2^(Δ) 1.5 p 1.5 p 1.5 p 1.5 p 4^(Δ) 1.5 1.5 p 1.5 p 1.5 p6^(Δ) 1.2 p 1.5 1.2 p 1.2 p 8^(Δ) 1.2 p 1.2 p 1.0 p 1.0 p 10^(Δ)  1.21.2 1.0 0.9

TABLE 4 No. 3 38 years old Male R L B Naked eye vision 0.3 0.5 0.5Corrected vision 1.2 1.2 1.5 ν_(d) = 59.2 ν_(d) = 40.9 ν_(d) = 40.2ν_(d) = 31.0 2^(Δ) 1.5 1.5 1.5 1.5 4^(Δ) 1.5 1.5 1.5 1.2 6^(Δ) 1.5 1.51.2 p 1.2 8^(Δ) 1.5 1.2 p 1.2 p 1.0 p 10^(Δ)  1.2 1.2 1.2 1.0

TABLE 5 No. 4 50 years old Male R L B Naked eye vision 1.2 1.2 1.5Corrected vision 1.2 1.2 1.5 ν_(d) = 59.2 ν_(d) = 40.9 ν_(d) = 40.2ν_(d) = 31.0 2^(Δ) 1.5 1.5 1.5 1.5 4^(Δ) 1.5 1.5 1.2 p 1.2 p 6^(Δ) 1.2 p1.5 1.2 p 1.2 8^(Δ) 1.2 1.0 p 1.2 1.0 10^(Δ)  1.0 1.0 1.0 0.8

TABLE 6 No. 5 36 years old Male R L B Naked eye vision 1.2 0.6 1.2Corrected vision 1.2 1.2 1.5 ν_(d) = 59.2 ν_(d) = 40.9 ν_(d) = 40.2ν_(d) = 31.0 2^(Δ) 1.5 1.5 1.5 1.5 4^(Δ) 1.5 1.5 1.5 1.2 p 6^(Δ) 1.5 1.51.5 1.2 p 8^(Δ) 1.5 1.5 1.2 p 1.0 p 10^(Δ)  1.2 1.2 1.2 1.0

TABLE 7 No. 6 36 years old Male R L B Naked eye vision Using Using UsingSpectacles Spectacles Spectacle Corrected vision 1.5 1.2 1.5 ν_(d) =59.2 ν_(d) = 40.9 ν_(d) = 40.2 ν_(d) = 31.0 2^(Δ) 1.5 1.5 1.5 1.5 4^(Δ)1.5 1.5 1.5 1.2 6^(Δ) 1.5 1.2 1.2 0.9 8^(Δ) 1.5 0.9 0.9 0.8 10^(Δ)  1.00.8 0.8 0.7

TABLE 8 No. 7 29 years old Male R L B Naked eye vision 0.8 0.6 0.8Corrected vision 1.2 1.2 1.5 ν_(d) = 59.2 ν_(d) = 40.9 ν_(d) = 40.2ν_(d) = 31.0 2^(Δ) 1.5 1.2 p 1.5 1.5 4^(Δ) 1.5 1.2 p 1.2 p 1.5 6^(Δ) 1.2p 1.2 1.0 p 1.5 8^(Δ) 1.2 1.0 p 1.0 p 1.2 p 10^(Δ)  1.0 1.0 0.9 p 1.0

In Table 2 to Table 8, visual acuity values to which a code p is addedare intermediate values of the visual acuity values thereabove. Here,the reason of performing the visual acuity measurement on both eyes isto make the condition same as that while fitting spectacles. Note thatlenses of the same Abbe number are normally worn on both eyes.

Then, on a plane with a coordinate system on which the logMAR visualacuity is taken on the vertical axis and the chromatic aberration ofmagnification is taken on the horizontal axis, the visual acuitymeasurement data of Table 2 to Table 8 are plotted. The result thereofis shown in FIG. 2.

Values of the horizontal axis of FIG. 2 will be explained. The values ofthe horizontal axis can be obtained from the Abbe numbers on Table 1 andthe prism values (10^(Δ), 8^(Δ), 6^(Δ), 4^(Δ), 2^(Δ)) shown in Table 2to Table 8. For example, when the Abbe number υ_(d)=40.2 and the prismvalue=6^(Δ), the chromatic aberration of magnification is 0.149 which isobtained by dividing 6⁶ by 40.2. In other words, the unit of thechromatic aberration of magnification is prism diopter/Abbe number.

Note that, in FIG. 2, the chromatic aberration of magnification is ameasurement result on a “d” line. However, also on an “e” line, theprism value increases by approximately the same ratio by which the Abbenumber increases. Therefore, the value of the chromatic aberration ofmagnification in the case of the “e” line is substantially the samevalue as the above-described value, so that it does not affect thedescription hereafter.

Next, values of the vertical axis of FIG. 2 will be explained. Each ofthe seven subjects has different corrected vision. Accordingly, thecorrected vision (in unit of decimal visual acuity) of all the subjectsare normalized to 1.0. By this normalization, the effect of dispersiondue to visual acuity measurement conditions (for example, brightness ofa visual acuity chart, precision of a measured distance, and the like)is largely reduced. Then, the normalized values thereof are converted tologMAR visual acuity.

The reason of expressing the visual acuity by the [logMAR] unit is basedon a fact that most of biophenomena can be expressed using logarithms.In other words, as compared to the decimal visual acuity and thefraction visual acuity, the logarithmic visual acuity expresses thebiophenomena more faithfully. Note that the conversion from the decimalvisual acuity to the logMAR visual acuity can be performed by thefollowing equation.logMAR visual acuity=log₁₀(1/decimal visual acuity)

From the plots of FIG. 2, the following facts are perceived.

(1) It is found that there is a linear correlation between the chromaticaberration of magnification and the logMAR visual acuity for all thesubjects of No. 1 to No. 7. Since the logMAR visual acuity generallygets larger as the visual acuity gets lower, FIG. 2 shows that thelogMAR visual acuity deteriorates in proportion to the increase of thechromatic aberration of magnification. Incidentally, in FIG. 2, to makethe linear correlation easily understandable, approximation straightlines are added on the plots showing the visual acuity deteriorations ofthe subjects No. 2 and No. 3.

The plots of the normalized logMAR visual acuity and the chromaticaberration of magnification as shown in FIG. 2 are attempted first bythe inventor. The inventor has found from consideration of these plotsthat the deterioration of the logMAR visual acuity due to the chromaticaberration is substantially proportional to the chromatic aberration ofmagnification.

(2) The correlation between the chromatic aberration of magnificationand the logMAR visual acuity is largely different among individuals.From this fact, it is considerable that the correlation is related tothe naked eye vision. Correction lenses for hypermetropic subjects arepositive, so that they are more strongly affected by the chromaticaberration as compared to myopic subjects. In other words, thehypermetropic subjects (No. 2, No. 6) are more strongly affected by thechromatic aberration as compared to the myopic subject (No. 3). Asreasons thereof, first, since hypermetropic spectacles and myopicspectacles are both worn for the measurement, an effect of the chromaticaberration due to the difference of the spectacles is conceivable.Second, an effect of the chromatic aberration due to the differencebetween hypermetropic eyes and myopic eyes is conceivable. However,there remains a problem that the number of subjects is small.

(3) Due to a small field tritanopia phenomenon, the minimum visual anglefor perception of yellow and blue is defined as 13 [arc minutes], andthat of red and green as 8 [arc minutes] (Incidentally, the “small fieldtritanopia” is an ophthalmological term. Refer to the above-describeddocument 6). Consequently, the chromatic aberration of magnification bywhich blurs of colors are not recognized becomes approximately 0.2^(Δ)or lower. However, as shown in FIG. 2, although colors are not seen, thedeterioration of the logMAR visual acuity linearly occurs in a rangeequal to or lower than the chromatic aberration of magnification of0.2^(Δ). From this experiment, the inventor has found first that, evenwhen colors are not seen, the proportional relation between the logMARvisual acuity and the chromatic aberration of magnification continuesuntil the chromatic aberration of magnification becomes zero.

From an analysis of the experiment data as above, the deterioration ofthe visual acuity (logMAR visual acuity) due to the chromatic aberrationof magnification becomes apparent.

Incidentally, it is useful to be capable of combining the visual acuityfunction not by visual acuity measurement, but by calculation based oneyeball models. However, at the present time, there is no suitable modelfor evaluating imaging characteristics of eyeball optics, and it iscommonly believed that no appropriate model is known for quantitativelyobtaining a chromatic dispersion. (Refer to “Tastuteru Ryu, HisayukiKato, Hitoshi Ozu: Kussetsuritsu bunpu suishoutai niyoru hito mokeigan(Human eyeball model with gradient index crystalline lens), KOHGAKU(Optics), 30(6): 407-413, 2001” (hereinafter referred to as document8).) Further, in view of precision or the like, it is difficult to makea total visual model for visual acuity calculation including processingof the retina and processing in the brain. Therefore, the presentinvention adopts a technique to define the visual acuity function basedon actual measured visual data.

[Relation Between the Chromatic Aberration of Magnification, Aberrationsother than the Chromatic Aberration, and Visual Acuity]

As above, it is proved that the visual acuity deteriorates due to thechromatic aberration of magnification. Next, it will be explained how tocombine this deterioration with a deterioration due to aberrations otherthan the chromatic aberration of magnification. As for the combinationprinciple, the experiment data in the above-described document 1 isreviewed, a part of the data being re-adjusted while new data beingadded, and a novel conclusion is thereby found.

First, the experiment described in the above-mentioned document 1 willbe explained. In the document 1, as shown in FIG. 3, MTF measurement iscarried out while fitting spectacles and side directional vision. As aspectacle lens 4, four types of lenses (No. 1 to No. 4) respectivelyhaving a different Abbe number are used.

Note that the MTF (Modulation Transfer Function) expresses what kind ofoptical performance an optical system such as a lens has by a spatialfrequency. The MTF is a suitable method to quantitatively express thequality of an image reaching from an object (a moire pattern (stripe) inthis case) to the final process (an eye in this case).

The conditions of the experiment are shown in the document 1 as follows.

(1) As shown in FIG. 3, a mask 5 having a circular opening 51 with 8[mm] diameter is placed on a position 42 which is 20 [mm] aside from thecenter position 41 on an surface of the spectacle lens 4, and the MTFmeasurement is carried out.

(2) The visual field is a circular shape, and the visual angle is 4°.

(3) The diopter of the lens used is −6.50 [D].

(4) The distance from a rear vertex of the lens to the center ofrotation is 25 [mm].

(5) The subject is 26 years old, myopic, and having a corrected visionof 1.0.

(6) A moire pattern presentation device 6 is used to perform the MTFmeasurement while changing a spatial frequency of the pattern.

The measurement results of the document 1 are the only publicly knowndata under a condition that the visual acuity deterioration due to thechromatic aberration of magnification and the visual acuitydeterioration due to aberrations (a power error, an astigmatism) whichaffect the visual acuity other than the chromatic aberration ofmagnification are combined. Refractive indexes and Abbe numbers of thelens 4 used in this experiment are shown in Table 9.

TABLE 9 Refractive index Abbe number (d line) (d line) No. 1 1.7020 29.8No. 2 1.7015 41.1 No. 3 1.7000 48.1 No. 4 1.6968 55.5

As shown in FIG. 9, for all the lenses of No. 1 to No. 4, the refractiveindexes are defined so as to have an average value of 1.700.Accordingly, visual acuity deteriorations due to the refractive indexesbecome substantially the same for all the lenses. Then, changes ofvisual acuity deterioration only due to the Abbe numbers are obtained bythe experiment. The results of the visual acuity measurement are shownin FIG. 10 of the document 1, which is shown in FIG. 4 as a reference.FIG. 4 is a graph on which cut-off frequencies are taken on the verticalaxis, and the inverse numbers of the Abbe numbers are taken on thehorizontal axis.

In order to make visual acuity deterioration data of FIG. 4 comparablewith visual acuity deterioration data only due to the chromaticaberration of magnification, the data of FIG. 4 are re-plotted andadjusted to be the same format as FIG. 2 so that a relation between thevisual acuity and the chromatic aberration of magnification can beeasily associated. The method of re-plotting is as follows.

Values for the vertical axis are obtained as follows. First, from FIG.4, cut-off frequency data at the lens center 41 and at the position 42which is 20 [mm] aside from the center are precisely read. Then, inorder to make the cut-off frequency data at the center of the lenses No.1 to No. 4 become zero for logMAR visual acuity, the cut-off frequencydata at the position 42 which is 20 [mm] aside from the center arenormalized to visual acuity deterioration data in logMAR unit. By thisnormalization, contributing factors for errors such as mechanic myopia,index luminance, index distance and the like under the conditions of theexperiment are largely reduced. The values of the vertical axis are thusobtained.

Values for the horizontal axis are obtained as follows. First, theinverse numbers (1/υd) of the Abbe numbers which are the horizontal axisof FIG. 4 are converted to the prism value/Abbe number, which is theunit of the chromatic aberration of magnification. However, prism dataof the lens opening at the position 42 which is 20 [mm] aside from thecenter are not described in the document 1. Further, although form dataof the spectacle lens 4 used in the experiment are needed in order toobtain the prism data by calculation, the form data are not described inthe document 1.

Accordingly, the prism value at the position 42 which is 20 [mm] asidefrom the center of the spectacle lens 4 used in the experiment isestimated. For this purpose, the following factors are presumed.

(1) First, the spectacle lens at the time the experiment was performedis a spherical lens.

(2) Second, even when the form of the spectacle lens used for theexperiment is presumed to be the same form as a form of spectacle lensmade of glass having a refractive index of 1.702 which is sold at thetime, the deviation angle and the prism value of a ray at the positionwhich is 20 [mm] aside from the lens center has substantially noinfluence on the description herein. The reason thereof is that theprism value at a position apart from the center of a lens does notlargely change due to its lens form. This is based on Prentice's formulawhich presents that the prism value at a position which is apart fromthe center of a lens is approximately proportional to the diopter at thecenter of the lens and a distance from the center to the position.

(3) Further, even when all the refractive indexes are presumed to be1.700, regarding the diopter at the center of a lens, the spectaclelenses No. 1 to No. 4 have errors at the central diopter ofapproximately 0.01 [D], which are not essentially different.

Here, the lens form data are presumed and shown in Table 10.

TABLE 10 Lens refractive index (d line) 1.700 Distance from rear vertexto center 25 of rotation (mm) Lens diopter (D) −6.50 Lens form Sphericalon front surface and rear surface Lens front surface curvature (1/mm)0.00609259 Lens rear surface curvature (1/mm) 0.01536412 Lens centerthickness 0.80

Using the data of this table 10, the prism value (prism diopter) at theposition which is 20 [mm] aside from the lens center can be calculatedas shown in Table 11.

TABLE 11 Prism (prism diopter) 15.72^(Δ)

Values obtained by dividing the prism diopter by the Abbe numbers ofrespective lenses No. 1 to No. 4 are defined as the chromatic aberrationof magnification. Accordingly, the inverse numbers of the Abbe numberswhich are the horizontal axis of FIG. 4 can be converted to the prismvalue/Abbe number, which is the regular unit of the chromatic aberrationof magnification. The values for the horizontal axis are thus obtained.

Here, data obtained by re-calculating the data of FIG. 4 as describedabove are shown in Table 12.

TABLE 12 The number of stripes at the The number of logMAR Chromaticposition 20 mm stripes at the visual acuity at Abbe aberration of asidecenter the position 20 mm number magnification (cycles/degree)(cycles/degree) aside No. 1 29.8 0.527 23.125 49.375 0.329 No. 2 41.10.382 28.125 48.750 0.239 No. 3 48.1 0.327 32.50 55.00 0.228 No. 4 55.50.283 36.25 53.125 0.166

The chromatic aberration of magnification in Table 12 is taken ashorizontal axis values, and the logMAR visual acuity at the position 20[mm] aside from the center is taken as vertical axis values, therebyobtaining data of the same format as FIG. 2.

[Calculation of Visual Acuity Deterioration Due to Off-Axis Aberrationwithout Chromatic Aberration]

Incidentally, in document 1, as shown in FIG. 4, by taking the cut-offfrequencies on the vertical axis and the inverse numbers of the Abbenumbers on the horizontal axis, the cut-off frequencies when thechromatic aberration does not exist are presumed, it is attempted toconsider influences by the off-axis aberrations other than the chromaticaberration of magnification of a spectacle lens. However, as a result,the document 1 reaches a conclusion that the influences of the chromaticaberration and the other aberrations on a periphery of a spectacle lensare not separable only by the change of MTF.

[Consideration of Influences of the Off-Axis Aberration other than theChromatic Aberration of a Spectacle Lens on Visual Acuity]

Accordingly, with respect to the above-described conclusion, a method ofseparating the chromatic aberration and the other aberrations by thefollowing technique is found. The influences of the off-axis aberrationsother than the chromatic aberration of a spectacle lens on visual acuitycan be calculated by the following technique.

First, visual acuity data by actual measurement are used to newlyperform an analysis in order to understand visual acuity deteriorationdue to the off-axis aberration other than the chromatic aberration. As abasal document to connect the actual measured value of the visual acuityand the lens aberrations other than the chromatic aberration, “Peters,Henry B., The relationship between refractive error and visual acuity atthree age levels, Am. J. Optom. Physiol. Opt., 38: 194-198, 1961”(hereinafter referred to as document 9) is available. Here, regardingthe aberrations other than the chromatic aberration, it is presumed thatthe aberrations other than the main chromatic aberrations which affectthe visual acuity only include power errors and astigmatisms which areirrelevant to pupil diameters.

A view of the document 9 shows the result of visual acuity measurementof a subject who regularly uses spectacles, the measurement beingcarried out with the spectacles taken off. The diagram is referredherein and shown in FIG. 5. This view shows values of the visual acuitymeasurement in unit of decimal visual acuity, on which sphericaldiopters are taken on the horizontal axis and astigmatic diopters aretaken on the vertical axis. Visual acuity deterioration occurs of courseand the subject is not able to see very well since the spectacles aretaken off. Note that, since it is the visual acuity measurementperformed in a state that the spectacles are not worn, an axialchromatic aberration of an eyeball does not affect visual acuity asmentioned in the above-described document 1, so that the visual acuitydeterioration data are not affected by the chromatic aberration.

Using these data, the visual acuity deterioration under a conditionexcluding the chromatic aberration is calculated. At this time, it isassumed that the visual acuity deterioration in a state that the subjectis not fitting spectacles is the same as the visual acuity deteriorationin a state that the subject is fitting spectacles and further lookingthrough lenses having inverse values of spherical diopter and astigmaticdiopter of the spectacle lenses.

Thus, while values of the visual acuity deterioration data of FIG. 5 areleft unchanged, and when signs of the spherical diopters on thehorizontal axis and the astigmatic diopters on the vertical axis arerespectively inversed, the resultant data represent visual acuitydeterioration in the case that an emmetropic subject is fittingspectacles having the inversed spherical diopter and astigmatic diopter.

Here, a relation between the visual acuity deterioration and the eyeballmotion (Listing's Law) will be explained. The Listing's Law means thatthere is a rotation axis of an eyeball motion in a plain (Listing'ssurface) perpendicular to an eye position including a center of thecycloduction when the eyeball looks far forward (first eye position).

In the measurement of the chromatic aberration of magnification in theabove-described document 1, the spherical diopter of the lens is −6.50[D]. However, it can be generally presumed that there is an astigmaticdiopter. For the case that there is an astigmatic diopter, a designingsystem in consideration of the Listing's Law is known (refer to JapanesePatent Laid-open No. Sho 57-10112).

However, in this publication, only an aberration derived by opticalcalculation is evaluated, and a relation with visual acuity is notdescribed. Hereinafter, the Listing's Law will be briefly explainedusing this publication.

According to the Listing's Law, with astigmatic spectacles being worn,when an eyeball rotates from the first eye position along a spectacleprincipal meridian in accordance with the Listing's Law, the spectacleprincipal meridian and the axis of a coordinate system of the rotationin accordance with the Listing's Law becomes parallel to each other, sothat the angle there between becomes zero.

However, when the eyeball changes to a direction different from thespectacle principal meridian, the angle between the spectacle principalmeridian and the axis of a coordinate system of the rotation does notbecome zero. In such a case, an angle displacement similar to that inthe above-described publication occurs.

By considering this angle displacement of the coordinate system, aprecise power error and astigmatism can be calculated. Typically, evenwhen it is an astigmatism which has the same absolute value as theabsolute value of a reference astigmatism (an astigmatic amount andastigmatic axis at the lens center), the astigmatism has adirectionality similar to vector values, so that a new astigmatism of avalue which is not zero arises. Hereinafter, this astigmatism isreferred to as a residual astigmatism. Incidentally, that the powererror is invariable for coordinate changes due to the Listing's Law.

Here, relations of the power error and the residual astigmatism, whichare off-axis aberrations of spectacle lenses, with the spherical diopterand the astigmatic diopter will be described. By considering thespherical diopter and the astigmatism diopter as aberration amounts,there are relations of the following equations when the residualastigmatism and the astigmatism diopter are positive. Also, when theresidual astigmatism and the astigmatism diopter are negative, it isonly for definition and there is no physical difference.Spherical diopter=power error−residual astigmatism/2   (1)Astigmatic diopter=residual astigmatism   (2)

Next, when seeing FIG. 5, it is clear that values of the horizontal axis(spherical diopter) are not symmetrical with respect to the origin.Further, values of the vertical axis (astigmatic diopter) also havenonlinear data peculiar to a living human body. For example, when visualacuity values with the same absolute value on the horizontal axis andwith different signs are examined, it is clear that a functionalrelation is not simple. In other words, the visual acuity value isnonlinear with respect to the optical performance value. Therefore, thenonlinear nature peculiar to the living human body needs to be takeninto consideration.

Thus, in the present invention, an interpolation function V is firstcalculated from the data of FIG. 5. Specifically, the horizontal axisvalues (spherical diopter) and the vertical axis values (astigmaticdiopter) are respectively scaled for 0.1 to 1 diopter, and visual acuityvalues are discretely plotted. Then, by interpolating the visual acuityvalues on the plane coordinate using a generally known interpolationmethod, the interpolation function V including the spherical diopter andthe astigmatic diopter as parameters is calculated. The interpolationfunction V is expressed by the following equation:first interpolation function V=V (spherical diopter, astigmatic diopter)  (3)

According to this equation (3), when the spherical diopter andastigmatic diopter as parameters are continuous values, a value of theinterpolation function V can be calculated. The value of theinterpolation function is the fraction visual acuity (=decimal visualacuity).

By substituting the spherical diopter and the astigmatic diopter of thisequation (3) with the equations (1) and (2) respectively, the followingequation (4) is obtained.second interpolation function V=V (power error, residual astigmatism)  (4)

According to this equation (4), the power error and the residualastigmatism obtained by optical calculation are correlated to the valueof the interpolation function. The value of the interpolation functionis the fraction visual acuity (=decimal visual acuity).

The second interpolation function V of this equation (4) can be used asit is as the visual acuity function in unit of the fraction visualacuity (decimal visual acuity). However, this function has a strongnonlinearity and also has no physical meaning, so that it is hardly inthe best state for optimization calculation. Accordingly, as thefollowing equation (5), it is preferable to convert the unit of theequation (4) to the logMAR, which is generally adopted nowadays.first visual acuity function [logMAR]=log₁₀ (1/V (power error, residualastigmatism))   (5)

Through the above processing, the visual acuity function in which thenonlinear nature of a living human body from the optical performancepoint of view is taken into consideration is derived (refer toInternational Patent Application of the inventor of the presentinvention, PCT/JP 02/04244: P11-P22, FIG. 1 to FIG. 12). The visualacuity of the living human body of course changes largely depending onage, a measurement environment, and so forth. In fact, however, theabove-described basic method requires a large calculation amount in theoptimization calculation. Therefore, instead of the above-describedequation (5), an approximate equation such as the following equation (6)can be used:second visual acuity function=αX[(power error)²+(K×residualastigmatism/2)²]^(1/2)   (6)

where, α is a coefficient within a range of 0.25≦α≦0.65, preferably0.4751. K is a coefficient within a range of 0.2≦K<1.

Using this equation (6), the power error, residual astigmatism, andvisual acuity at a position which is 20 [mm] aside from the lens centerare calculated with the conditions shown in Table 10. Consequently,visual acuity when there is no influence of the chromatic aberration iscalculated. The obtained data are shown in Table 13.

TABLE 13 Power error (dptr) 0.167 Residual astigmatism (dptr) 0.419Visual acuity (logMAR) 0.127

FIG. 6 is a view showing plots of data based on Tables 12 and 13(hereinafter referred to as “combination data 1”) which are newly addedto FIG. 2 by the inventor of the present invention, in which visualacuity deteriorations of the chromatic aberration of magnification andthe other aberration are combined. In the data (chromatic aberration ofmagnification) of Table 12 derived from the document 1, the linearrelation described during the consideration of FIG. 2 is derived. Also,a segment visual acuity when the chromatic aberration of magnificationon the horizontal axis becomes zero should be 0.127 as shown in Table13. Specifically, the numeric values are adopted from results ofmeasurement data of 7251 persons.

Therefore, even when the visual acuity function (6) of approximateequation is used, the data is remarkably reliable as against the otherdata. Then, in FIG. 6, the combination of visual acuity deteriorationsof the chromatic aberration of magnification and the other aberration isa straight line which passes through the horizontal axis 0 (zero) andthe vertical axis 0.127 (hereinafter referred to as a “combinationstraight line 1”).

Further, the combination straight line is obtained by a substantiallyparallel movement of the approximation straight line of the data ofsubject No. 3 (refractive index 1.7000, Abbe number 48.1) among the dataof visual acuity deterioration. That is to say, in FIG. 6, thecombination straight line, which is obtained under a condition that thechromatic aberration of magnification and the other aberration bothaffect the visual acuity, is obtained by shifting the approximationstraight line of the data of subject No. 3, which is obtained under acondition that only the chromatic aberration of magnification affectsthe visual acuity, upward by the segment visual acuity which is thevisual acuity when only the aberrations other than the chromaticaberration of magnification affected the visual acuity.

[Conclusion]

From this fact, the inventor has found first that, in order to expressvisual acuity in [logMAR] unit, the deterioration of visual acuitywithout chromatic aberration should be simply added to the deteriorationof visual acuity due to chromatic aberration.

Next, in order to verify the conclusion, data of a cut-off frequency ata position which is 10 [mm] aside from the center of FIG. 11 of thedocument 1 are modified by a technique similar to that of calculatingthe data of Table 12 and then adopted. In other words, logMAR, chromaticaberration of magnification, normalization of visual acuity data, andvisual acuity calculation when there is no chromatic aberration areperformed. This data shows the data calculated from data of No. 1, 4shown in FIG. 11.

First, the form data of Table 10 are used to calculate the cut-offfrequencies at 10 [mm] from the center. This data is shown in Table 14.

TABLE 14 Prism (prism diopter) 6.68^(Δ)

Using this data, the normalized cut-off frequency of FIG. 11 of thedocument 1 are shown in Table 15.

TABLE 15 The number of stripes at the logMAR Chromatic position 10 mmThe number visual acuity aberration of aside of stripes at at theposition Abbe number magnification (cycles/degree) the center 10 mmaside No. 1 29.8 0.224 32.449 49.375 0.182 No. 4 55.5 0.120 43.06153.125 0.091

The power error, the astigmatism, the visual acuity without chromaticaberration at 10 [mm] from the center are shown in Table 16.

TABLE 16 Power error (dptr) 0.023 Residual astigmatism (dptr) 0.196Visual Acuity 0.048

Here, values obtained by subtracting the visual acuity without chromaticaberration of Table 13 from the values of the logMAR visual acuity at 20[mm] of Table 12 can be treated as the chromatic aberration ofmagnification itself. In other words, the values become the same formatas FIG. 2. Similarly, values obtained by subtracting the visual acuityvalue of Table 16 from the logMAR visual acuity at 10 [mm] from thecenter of Table 15 become the same format as FIG. 2. These values areshown in Table 17.

TABLE 17 Visual acuity from which an influence other than chromaticChromatic aberration aberration of magnification is of magnificationsubtracted No. 4 (10 mm) 0.120 0.043 No. 1 (10 mm) 0.224 0.134 No. 4 (20mm) 0.283 0.039 No. 3 (20 mm) 0.327 0.101 No. 2 (20 mm) 0.382 0.112 No.1 (20 mm) 0.527 0.202

The data of this Table 17 (hereinafter referred to as “combination data2”) displayed simultaneously with the data of FIG. 2 becomes FIG. 7. InFIG. 7, approximation straight lines of plots of the combination data 2(hereinafter referred to as a “combination straight line 2”) are alsoshown. From FIG. 7, the deterioration of logMAR visual acuity isproportional to the chromatic aberration of magnification, and it isproved to be proportional even in a range of the chromatic aberration ofmagnification of 0.2 or lower. From the above data, it can be verifiedthat the sum of the visual acuity deterioration only due to aberrationsother than the chromatic aberration and the deterioration of the visualacuity only due to the chromatic aberration is the total deteriorationof the visual acuity.

To express this finding by numerical expression, a term of the chromaticaberration of magnification is added to the equation (6), providing thefollowing equation (7):third visual acuity function=α×[(power error)²+(K×residualastigmatism)²]^(1/2)+β×chromatic aberration of magnification   (7)

where, α is a coefficient within a range of 0.25≦α≦0.65, preferably0.4751. β is a coefficient varying depending on each person within arange of 0.2≦β≦1.2, preferably 0.2≦β≦1.0, more preferably 0.6. Note thatvalues of α and β respectively vary from measured data numbers. K is acoefficient within a range of 0.2≦K<1, preferably 0.2≦K<0.6.

Here, as an optical value related to the chromatic aberration ofmagnification, a residual prism is defined. The residual prism is anamount which has a prism direction measured from a coordinate system inaccordance with the Listing's Law. The absolute value thereof is used inthe equation (7). The chromatic aberration of magnification in theequation (7) is a value obtained by dividing the absolute value of theresidual prism by an Abbe number.

Since the Listing's Law is taken into consideration in the visual acuityfunction of the equation (7), it can faithfully express visual acuitywhen used for design or evaluation of astigmatic lenses or the like.

Note that the equation (7) can be applied to spherical lenses. However,on the principal meridian of a spherical lens, the value of the residualastigmatism becomes equivalent to the astigmatism, so that the Listing'sLaw should not necessarily be considered in design or evaluation of thespherical lens. Accordingly, a visual acuity function of the followingequation (8) may be applied to the spherical lenses:fourth visual acuity function=α×[(power error)²+(K×residualastigmatism)²]^(1/2)+β×chromatic aberration of magnification   (8)

where, α is a coefficient within a range of 0.25≦α≦0.65, preferably0.4751. β is a coefficient varying depending on each person within arange of 0.2≦β≦1.2, preferably 0.2≦β≦1.0, more preferably 0.6. Note thatvalues of α and β respectively vary from measured data numbers. K is acoefficient within a range of 0.2≦K<1, preferably 0.2≦K<0.6.

[Application of the Visual Acuity Functions to Designing of Lenses]

As described above, in the process of correcting aberrations in anoptical system, a common designing method is to minimally calculate amerit function, which is composed by evaluation functions of severalaberrations and lens forms, by a known optimization calculation (forexample, Japanese Examined Patent Publication No. Hei 02-38930).

First, various types of evaluation indexes can be incorporated as thefactors configuring the merit function. For example, aberrations whichshould be corrected for spectacles include distortion aberration, thoughit is not directly related to the visual acuity value. The distortionaberration is widely known as a cause of sway and distortion mainlyduring initial period of fitting spectacles.

Conventionally, the distortion of spectacles are expressed as a visualangle magnification M (refer to “Kazuo Miyake: Futatabi kakubairitsunitsuite (On Angle Magnification Again), KOHGAKU (OPTICS) Vol. 19, No.10”) (hereinafter referred to as document 10). When expressing thevisual angle magnification as M₀ by an equation, it becomes:M ₀=lim_(exit angle→0)(tan(exit angle)/tan(incident angle))   (9)

Here, M₀ can be easily calculated by paraxial optical calculation. M₀will be simply explained. When an exit ray passes the center of aneyeball entrance pupil, M₀ is usually called a spectacle magnification.However, when the exit ray passes a center of cycloduction, it is moreappropriate to be called a rotation visual angle magnification,imitating Miyake of the document 10.

Further, letting a visual angle magnification of a peripheral portion beM,M=tan(exit angle)/tan(incident angle)   (10)

Then, the distortion aberration (DIST) of spectacles is expressed as thefollowing equation (11) using the equations (9), (10):DIST=100×((M/M ₀)−1)   (11)

The equation (11) is a relational expression which has beenconventionally derived. Normally, the exit ray passes the center ofcycloduction, and the DIST is called a dynamic distortion aberration ofspectacles.

Here, the equation (11) is studied from a designing method in which aneyeball motion is taken into consideration. Similarly to the explanationof the residual astigmatism and the residual prism, even when it is thesame DIST, a residual DIST occurs due to a difference of axial directionsince the DIST is a vector value.

In other words, the conventional M₀ and M are calculated, as DIST whenthey have the same direction as a condition in a background. Forexample, when M₀ and M in the same direction are the same amount, it iscalculated as DIST=0 by the equation (11). Since the calculation includethe above-mentioned angle displacement generated by the eyeball motion,M₀ and M are extendedly defined naturally as vector amounts.

Then, when the lens is an astigmatic lens, M₀ becomes a vector valuehaving a different value in the radiation direction at a lens diopterreference point (usually, the center part of a lens). At a lensevaluation point of optimization calculation, a residual visual anglemagnification is defined as a value obtained by subtracting the centralvisual angle magnification from the visual angle magnification.

In other words, when the residual visual angle magnification=M−M₀, andthe Sign is defined as a positive/negative sign of a scalar product ofthe residual visual angle magnification and M₀, the extended definitionof the distortion aberration of spectacles of the present invention inwhich the Listing's Law is taken into consideration becomes thefollowing equations (12), (13). Further, the relation thereof is shownin FIG. 8.Residual visual angle magnification=visual angle magnification M−visualangle magnification M ₀   (12)Extended DIST=Sign×100×(|residual visual angle magnification|/|visualangle magnification M ₀|)   (13)

In the spectacle lens designing of the present invention, calculation isperformed by the ray tracing method while letting a ray pass a lens,where the equations (7), (13) are calculated at respective evaluationpoints of the lens.

Note that the evaluation points are plural virtual points which are seton a spectacle lens in order to evaluate an optical performance of thespectacle lens. The evaluation points can be set to approximately 5 to10 points for an axially symmetric lens and approximately 15 to 10000points for an axially asymmetric lens.

In the case of the equation (7), different values are obtained dependingon the evaluated object distance. Which object distance to be taken isdependent on a lens characteristic and discretion of designer. Forexample, strictly speaking, there is no actually measured visual acuityvalue of near vision in the following equation (14), but responses tothe power error and the residual astigmatism are calculated assumingthat they are similar to those of the visual acuity of far vision of theequation (7).

The dynamic distortion aberration of spectacles is not theoreticallyrelated to the distance, but the one for which no clear judgmentmaterial on how to distribute visual acuity and distortion is availableis also dependent on the discretion of a designer. From the above, amerit function of single evaluation rate scale, which is a combinedfunction of general evaluation functions of the present invention,becomes the following equation (14).

$\begin{matrix}\begin{matrix}\lbrack {{Equation}\mspace{14mu} 3} \rbrack \\{{{merit}\mspace{14mu}{function}} = {{a \times {\sum\limits_{n = 1}^{m}\;( {{u_{n} \cdot {far}}\mspace{14mu}{vision}_{n}} )^{2}}} +}} \\{{\mspace{191mu}}{{b{\sum\limits_{n = 1}^{m}\;( {{v_{n} \cdot {near}}\mspace{14mu}{vision}_{n}} )^{2}}} +}} \\{\mspace{191mu}{c \times {\sum\limits_{n = 1}^{m}\;( {w_{n} \cdot {DIST}_{n}} )^{2}}}}\end{matrix} & (14)\end{matrix}$

where, m is a natural number expressing the number of set evaluationpoints, n is a natural number assigned to the respective evaluationpoints, the far vision is a value when looking a far region of a visualacuity function at the evaluation point, and the near vision is a valuewhen looking a near region of a visual acuity function at the evaluationpoint. The visual acuity function used in this equation (14) is theequation (7) which includes the chromatic aberration.

Further, a, b, c are predetermined coefficients respectively expressingweight distribution of the respective terms in the equation (14), and u,v, w are coefficients respectively expressing weight distribution of therespective evaluation points. Note that the weight includes the conceptzero. However, zero is not adopted here as the weight.

Here, the far region can be defined as, for example, a range from areference point to a far point of 10 [m] to infinity. An expression ofthis range in diopter unit is 0 [D] to 0.1 [D]. Further, the near regioncan be defined as, for example, a range between the reference point and30 [cm] to 33 [cm]. An expression of this range in diopter unit isapproximately 3 [D] to 3.33 [D]. Further, there is no uniform standardto determine where should the reference point be, but it is normally atthe center of cycloduction, a lens surface, or the center of cornea.

Since the Listing's Law is taken into consideration in the equation(14), evaluation or design which is more faithful to visual acuity canbe performed when the equation (14) is applied to an astigmatic lens orthe like.

Note that the equation (14) can be applied to spherical lenses. However,on the principal meridian of a spherical lens, the value of the residualastigmatism becomes equivalent to the astigmatism, and the residual DISTbecomes equivalent to the DIST (distortion aberration), the Listing'sLaw should not necessarily be considered in design or evaluation of thespherical lens. Accordingly, a merit function of the following equation(15) can be applied to the spherical lenses:

$\begin{matrix}\begin{matrix}\lbrack {{Equation}\mspace{14mu} 4} \rbrack \\{{{merit}\mspace{14mu}{function}} = {{a \times {\sum\limits_{n = 1}^{m}\;( {{u_{n} \cdot {far}}\mspace{14mu}{vision}_{n}} )^{2}}} +}} \\{{\mspace{191mu}}{{b{\sum\limits_{n = 1}^{m}\;( {{v_{n} \cdot {near}}\mspace{14mu}{vision}_{n}} )^{2}}} +}} \\{\mspace{191mu}{c \times {\sum\limits_{n = 1}^{m}\;( {w_{n} \cdot \;{DIST}_{n}} )^{2}}}}\end{matrix} & (15)\end{matrix}$

where, m is a natural number expressing the number of set evaluationpoints; n is a natural number assigned to the respective evaluationpoints; the far vision is a value when looking a far region of a visualacuity function at the evaluation point; the near vision is a value whenlooking a near region of a visual acuity function at the evaluationpoint; DIST is a value of the distortion aberration at the evaluationpoint; a, b, c, are predetermined coefficients respectively expressingweight distribution of the respective terms in the equation (15); and u,v, w, are coefficients respectively expressing weight distribution ofthe respective evaluation points.

A characteristic, aesthetic, economic, and optical consideration and thelike of the lens are carried out to design a good lens, and the weightdistribution is performed and determined by the discretion of adesigner. Further, there is also a case in which a term such as a lensform which is not directly relevant to visual acuity is added to themerit function. Such a case is also within the scope of the presentinvention when the above-described equation is the main factor therein.

When the chromatic aberration is positively shown (directly expressed)on the merit function, it becomes the following equation:

$\begin{matrix}\begin{matrix}\lbrack {{Equation}\mspace{14mu} 5} \rbrack \\{{{merit}\mspace{14mu}{function}} = {{a \times {\sum\limits_{n}\;( {{u_{n} \cdot {far}}\mspace{14mu}{vision}_{n}} )^{2}}} +}} \\{{\mspace{191mu}}{{b{\sum\limits_{n}\;( {{v_{n} \cdot {near}}\mspace{14mu}{vision}_{n}} )^{2}}} +}} \\{\mspace{185mu}{{c \times {\sum\limits_{n}\;( {{w_{n} \cdot {residual}}\mspace{14mu}{DIST}_{n}} )^{2}}} +}} \\{\mspace{185mu}{d \times {\sum\limits_{n}( {{s_{n} \cdot {chromatic}}\mspace{14mu}{aberration}} }}} \\ \mspace{185mu}{{of}\mspace{14mu}{magnification}_{n}} )^{2}\end{matrix} & (16)\end{matrix}$

The visual acuity function in the equation (16) is the function (6)which does not include the chromatic aberration. a, b, c, d are weightdistribution at respective evaluation functions. u, v, w, s are weightdistribution at respective evaluation points. n is the evaluation pointof the spectacle lens. The ratio of a, b in the equation (16) is that ofthe α, β in the equation (7).

The merit functions in this equation (16) is also substantiallyequivalent to the equation (14). Further, the merit function in whichDIST is adopted instead of the residual DIST in the equation (16) issubstantially equivalent to the equation (15).

The merit function will be studied from the viewpoint of the degree ofdesigning freedom. When a spectacle lens design in which a front surfaceand a rear surface of the lens are free curved surfaces which can berestrictively transformed freely under a condition that the diopter ofthe lens is fixed is used, a first term of a second term of the meritfunction can be satisfied by a combination of transformation of the twosurfaces. Specifically, at a certain object distance, a power error anda residual astigmatism which are constituent factors of the visualacuity function can be both made zero.

However, under a restrictive condition that the front surface which isone of surfaces of a lens is axially symmetric lens in aesthetic andeconomic aspects, it is not possible to make both the power error andthe residual astigmatism at a certain object distance zero on the entiresurface (both surfaces) of the spectacle lens. Still more, generally itis difficult to make the chromatic aberration of magnification and theresidual DIST zero in the surface structure having a diopter, withoutinfluencing other evaluation functions.

Therefore, coefficients and weights are dependent on the discretion of alens designer. Further, from the viewpoint of the degree of designingfreedom, when the front surface is fixed to be spherical or the like,the freedom of the designer is limited, and it becomes difficult tocontrol the residual DIST which is the third term in the merit function.To explain this further, when it is possible for the designer to freelytransform the front surface and the rear surface of the spectacle lens,the merit function which is the function of the surface thereof can befreely controlled, whereas, when there is a designing restriction suchas the spherical surface, it influences the minimization of the meritfunction.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a schematic view of a measurement experiment which isperformed for obtaining visual acuity deterioration due to chromaticaberration of magnification;

FIG. 2 is a view showing the visual acuity deterioration due to thechromatic aberration of magnification;

FIG. 3 is a schematic view of a measurement experiment which isperformed for obtaining a combination principle of the visual acuitydeterioration due to the chromatic aberration of magnification andvisual acuity deterioration due to aberrations other than the chromaticaberration;

FIG. 4 is a view showing FIG. 10 of the above-described document 1 byreference;

FIG. 5 is a view showing visual acuity measurement data of theabove-described document 9 by reference;

FIG. 6 is a view showing deterioration of combined visual acuity;

FIG. 7 is a view explaining recognition of the deterioration of thecombined visual acuity;

FIG. 8 is an explanatory view of a residual DIST;

FIG. 9 is an explanatory view of a clear visual angle and a clear visualdiameter;

FIG. 10 is a view showing a relation between the clear visual diameterof a spectacle lens and a diopter by each Abbe number;

FIG. 11 is a view showing a relation between the Abbe number necessaryfor a visual angle 30° to be a clear visual area and a diopter; and

FIG. 12 is a view showing a logMAR visual acuity in the visual angle of60° by each Abbe number.

EXPLANATION OF NUMERALS AND SYMBOLS

1 . . . international type visual acuity chart, 2 . . . prism, 3 . . .spectacle lens, 4 . . . spectacle lens, 41 . . . center of spectaclelens, 42 . . . side of spectacle lens, 5 . . . mask, 51 . . . circularopening, 6 . . . moire pattern presentation device, 10 . . . spectaclelens, 11 . . . optical axis, 12 . . . spherical cone, 13 . . . center ofcycloduction (center of rotation of an eyeball), 14 . . . rear vertex,15 . . . rear plane surface, θ . . . clear vision angle, R . . . clearvision diameter, VR . . . distance from the rear vertex to the center ofcycloduction.

BEST MODE FOR CARRYING OUT THE INVENTION

Hereinafter, embodiments of an evaluation method of the presentinvention will be explained. In the present invention, a lens designingmethod using a general, publicly known ray tracing method using acomputer is used, and an explanation of detailed designing method isomitted since it is the same as that described in the prior art.However, optical performance calculation and a displaying program of itsresults are composed including an after-mentioned processing programrelated to calculation and display of a clear visual angle and a clearvisual diameter.

EXAMPLE 1 Comparison of Clear Visual Diameter of Spectacle Lenses whenAbbe Numbers are Different

To begin with, the clear visual diameter will be explained. First, avisual acuity function of the equation (7) is used to define a clearvisual area of a spectacle lens. The clear visual area is an area of thespectacle lens which can be clearly seen. Incidentally, the clear visualarea is also referred to as, for example, a distinct visual area or astandard visual area.

Specifically, the clear visual area is defined based on a logMAR visualacuity value which is a value of the visual acuity function of theequation (7). In particular, when it can be most clearly seen when thevalue of the logMAR visual acuity is zero, a region preferably within arange of zero to 0.1 or 0.2 is defined as the clear visual area. Toexpress this region in decimal visual acuity, it becomes 1 toapproximately 0.6 or approximately 0.8. This range is a preferablereference value which can be evaluated as a visual acuity value by acommon sense. However, the logMAR visual acuity value which defines theclear visual area is not specifically limited, and it can be set withina range which does not depart from the object.

Hereinafter, in this example, a region in which the logMAR visual acuityis within 0.1 is defined as the clear visual area.

Next, a spherical cone which has a solid angle equal to a solid angle inwhich the clear visual area is expected from the center of rotation ofan eye (center of cycloduction ) and is axially symmetrical to anoptical axis of the spectacle lens is assumed, and the clear visualangle is obtained based on the spherical cone.

(incidentally, refer to Japanese Patent Application Laid-open No.2002-211641 for more detail)

Specifically, as shown in FIG. 9, a solid angle [steradian] iscalculated as a spherical cone 12 which is axially symmetrical to anoptical axis 11 of a spectacle lens 10. The spherical cone 12 has acenter of cycloduction 13 as the vertex, and a spherical surface part onthe spectacle lens 10 side.

When a vertex angle θ of this spherical cone 12 is calculated andexpressed as the clear visual angle in unit of angle, it becomes aneasily understandable expression format. The vertex angle θ of thespherical cone 12 means a vertex angle θ produced when the sphericalcone 12 is cut out by a plane surface which includes the optical axis11. Incidentally, the term “clear visual angle” is named by the inventorand can also be rephrased as, for example, average visual angle orequivalent visual angle.

Specifically, the clear visual angle can be approximately obtained bythe following equation (17). The reason to use the term “approximately”is because the proportional relation between the number of rays and thesolid angle is broken when the visual angle is large. However, since thesolid angle to the spectacle lens having a lens diameter (specifically,for example, a diameter of 80 [mm] or less) used in a general spectaclesindustry is small, and the above-mentioned proportional relation doesnot practically affect a lens, so that the following equation (17) canbe used without any problem.

$\begin{matrix}\begin{matrix}\lbrack {{Equation}\mspace{14mu} 6} \rbrack \\{{{clear}\mspace{14mu}{visual}\mspace{14mu}{angle}} \cong {2 \times L \times \sqrt{\frac{N}{\pi}}}}\end{matrix} & (17)\end{matrix}$

where, L is an angle interval when many rays incident from the center ofcycloduction 13 to the spectacle lens 10 with the same angle intervals(for example, 1° pitch), and N is the number of rays which pass theclear visual area among incident rays.

The value of the clear visual angle obtained as above is a value whichdoes not depend on the lens diameter, but depends on the absolute sizeof the clear visual area of the spectacle lens 10. This value of theclear visual angle can be preferably used as the optical performancevalue of the spectacle lens 10.

Next, in FIG. 9, it is calculated a value of a clear visual diameter Rcorresponding to the diameter R of a circle obtained by projecting thesolid angle of the spherical cone 12 on a plane surface 15 which isperpendicular to the optical axis 11 and includes a rear vertex 14 ofthe spectacle lens 10. The clear visual diameter R can be approximatelycalculated using the following equation (18) based on the clear visualangle (the equivalent visual angle) θ and a value of a distance VR fromthe rear vertex 14 to the center of cycloduction 13. Incidentally, theterm “clear visual diameter” is named by the inventor.clear visual diameter=2×VR×tan (clear visual angle/2)   (18)

Here, the clear visual angle is obtained by the above-described equation(17).

The values of the clear visual angle and the clear visual diameterdescribed above are values which express the absolute size of the clearvisual area of a spectacle lens. These values can be respectivelydisplayed in unit of angle and in unit of length, which can be easilyunderstood by a person who does not have specialized knowledge aboutlenses.

As above, the calculation method of the clear visual diameter has beenexplained. This method is applied to spectacle lenses shown in Table 18.These spectacle lenses are spherical lenses, and all have the samerefractive index (1.60). When calculating the clear visual diameter,calculation in which an eyeball motion (the Listing's Law) is taken intoconsideration is performed for comparison of astigmatic lenses. The usedequation (7) is calculated with 2.986 as α and 0.62 as β. Further, thedistance VR from the rear vertex of a lens to the center of cycloductionis calculated by the following equation:VR(mm)=27.0−(average diopter/6)   (19)

Then, values of the clear visual diameter respectively corresponding toeach of the diopters in Table 18 are calculated separately for the casesof no chromatic aberration, Abbe numbers 40 and 60. Results ofcalculation are shown in Table 19. Note that the diopter display inTables 18, 19 are all C minus display.

TABLE 18 Front Rear Rear surface surface surface Lens curvaturecurvature S curvature C Diopter S Diopter C diameter Thickness (1/mm)axis (1/mm) axis (1/mm) 8 −2 65 8.46 0.018264 0.006054 0.009388 7 −2 657.61 0.018264 0.007602 0.010935 6 −2 65 6.47 0.014642 0.005182 0.0085155 −2 65 5.61 0.014642 0.006774 0.010107 4 −2 70 5.19 0.01097 0.0045430.007876 3 −2 70 4.17 0.01097 0.006162 0.009495 2 −2 70 3.09 0.0091190.005883 0.009217 1 −2 75 2.7 0.009099 0.007517 0.01085 0 −2 75 20.009099 0.009161 0.012495 −1 −2 75 1.5 0.007281 0.008978 0.012311 −2 −275 1 0.007281 0.010634 0.013968 −3 −2 75 1 0.00532 0.010331 0.013664 −4−2 75 1 0.00532 0.011998 0.015331 −5 −2 70 1 0.003612 0.01195 0.015283−6 −2 70 1 0.003612 0.013616 0.01695 −7 −2 70 1 0.002144 0.0138120.017145 −8 −2 70 1 0.002144 0.015479 0.018812

TABLE 19 Clear Clear visual visual Clear visual diameter diameterdiameter (no (Abbe (Abbe Diopter Diopter Lens chromatic number number SC diameter aberration) 60) 30) 8 −2 65 30 15 10 7 −2 65 29 17 11 6 −2 6533 18 12 5 −2 65 36 23 16 4 −2 70 35 23 17 3 −2 70 42 31 24 2 −2 70 4436 31 1 −2 75 53 44 37 0 −2 75 66 51 42 −1 −2 75 64 39 29 −2 −2 75 59 3523 −3 −2 75 51 23 17 −4 −2 75 51 23 15 −5 −2 70 32 18 12 −6 −2 70 40 1812 −7 −2 70 28 15 10 −8 −2 70 35 15 9

Furthermore, the data of Table 19 are plotted and shown in FIG. 10. InFIG. 10, spherical diopters are taken on the horizontal axis, and lensdiameters (clear visual diameter) are taken on the vertical axis in [mm]unit. The lenses of respective diopters are all in the same form havingthe lens data of Table 12, and they are just comparisons of the clearvisual diameters in the cases of no chromatic aberration, Abbe numbers60 and 30. In FIG. 10, respective sequential line graphs connectingplots show lens diameters, the clear visual diameters in the case of nochromatic aberration, the clear visual diameters in the case of Abbenumber 60, and the clear visual diameters in the case of Abbe number 30,sequentially from the one having the largest lens diameter.

Here, the distance from the sequential line showing the lens diametersto the sequential line showing the clear visual diameter in the case ofno chromatic aberration indicates deterioration of visual acuity due tothe power error and the residual astigmatism. Further, the distance fromthe sequential line showing the clear visual diameter in the case of nochromatic aberration to the sequential line showing the clear visualdiameter in the case of Abbe number 60, or to the sequential lineshowing the clear visual diameter in the case of Abbe number 30indicates the deterioration of visual acuity due to the chromaticaberration of magnification.

Accordingly, based on FIG. 10, it is clear that the deterioration ofvisual acuity due to the chromatic aberration (chromatic aberration ofmagnification) is larger as compared to the power error and the residualastigmatism. This fact suggests that the chromatic aberration should notbe ignored for improvement of lens performance.

As above, the relation between the Abbe number and the clear visualdiameter has been explained. This example can be applied mainly tooptical performance calculation by Abbe number variations duringdevelopment of lens materials.

EXAMPLE 2 A Necessary Abbe Number for Visual Angle 30° to be Within theClear Visual Diameter

This example answers a question, how much degree of the Abbe number isnecessary during development of lens materials. Various data of lensesapplied in this example is shown in Table 20. Other calculationconditions are the same as those in Example 1.

The technique of calculation is performed in such a manner that the Abbenumber is gradually increased from a small value, and the calculation isstopped when it becomes the clear visual area at the visual angle of 30°(cycloduction angle of 15°). Here, the clear visual area is defined as aregion in which the logMAR visual acuity becomes 0.1 or lower. Resultsof the calculation are shown in Table 21 and FIG. 11.

TABLE 20 Front Rear Rear surface surface surface Lens curvaturecurvature S curvature C Diopter S Diopter C diameter Thickness (1/mm)axis (1/mm) axis (1/mm) 8 0 65 8.46 0.018264 0.006054 0.006054 7 0 657.61 0.018264 0.007602 0.007602 6 0 65 6.47 0.014642 0.005182 0.005182 50 65 5.61 0.014642 0.006774 0.006774 4 0 70 5.19 0.01097 0.0045430.004543 3 0 70 4.17 0.01097 0.006162 0.006162 2 0 70 3.09 0.0091190.005883 0.005883 1 0 75 2.7 0.009099 0.007517 0.007515 0 0 75 20.009099 0.009161 0.009161 −1 0 75 1.5 0.009099 0.0010812 0.010812 −2 075 1 0.009099 0.012463 0.012463 −3 0 75 1 0.007281 0.012301 0.012301 −40 75 1 0.007281 0.013968 0.013968 −5 0 75 1 0.00532 0.013664 0.013664 −60 75 1 0.00532 0.015331 0.015331 −7 0 70 1 0.003612 0.015283 0.015283 −80 70 1 0.003612 0.01695 0.01695

TABLE 21 Necessary Necessary Abbe number Abbe number (Clear visual(Quasi-clear Diopter S Diopter C area) visual area) 8 0 79 27 7 0 51 216 0 59 20 5 0 36 15 4 0 36 13 3 0 21 9 2 0 13 6 1 0 7 4 0 0 2 1 −1 0 4 2−2 0 9 5 −3 0 15 7 −4 0 20 10 −5 0 29 13 −6 0 33 15 −7 0 44 19 −8 0 4621

FIG. 11, diopters are taken on the horizontal axis, and necessary Abbenumbers to be in the clear visual area at the visual angle of 30°(cycloduction angle of 15°) are taken on the vertical axis. As shown inFIG. 11, dependence of the necessary Abbe number on the lens dioptersare presented quantitatively.

Further, from FIG. 11, it is perceived that, for example, the Abbenumber 40 can satisfy the visual angle of 30° by approximately −6.5 [D]to +5 [D]. In Table 21, the vertical axis shows necessary Abbe numbersto be in a quasi-clear visual area at the visual angle of 30°(cycloduction angle of 15°). Here, the quasi-clear visual area isdefined as a region in which the logMAR visual acuity is within 0.2.

As above, it has become clear that how much degree of the Abbe number isnecessary for how much degree of the angle. Therefore, it can be saidthat the equation (7) becomes crucial judgment standard for the designof spectacle lenses and the development of materials.

EXAMPLE 3 Visual Acuity Evaluation at Visual Angle of 60° (CycloductionAngle of 30°)

In many documents in the past, spectacle lenses are designed to havereduced aberrations at the cycloduction angle of 30°, or thecycloduction angle of 30° is used as a measure for correctingaberrations. From a viewpoint of visual acuity, performance evaluationat a visual angle of 60° is crucial. Accordingly, the various lens dataof Table 20 are used as lens from data, and logMAR visual acuity at thevisual angle of 60° (cycloduction angle of 30°) is calculated. Resultsof the calculation are shown in Table 22 and FIG. 12.

TABLE 22 No chromatic Abbe Abbe Diopter S Diopter C aberration number 60number 30 Power error Astigmatism 8 0 0.21 0.36 0.51 0.23 0.75 7 0 0.120.25 0.38 0.04 0.48 6 0 0.21 0.32 0.43 0.28 0.67 5 0 0.11 0.21 0.3 0.110.42 4 0 0.19 0.26 0.34 0.28 0.54 3 0 0.1 0.16 0.22 0.13 0.32 2 0 0.080.12 0.16 0.12 0.24 1 0 0.02 0.05 0.07 0.02 0.08 0 0 0.01 0.02 0.02−0.02 0.02 −1 0 0.02 0.04 0.05 −0.03 0.08 −2 0 0.02 0.05 0.09 0.01 0.09−3 0 0.04 0.09 0.14 −0.02 0.17 −4 0 0.04 0.11 0.18 0.04 0.15 −5 0 0.060.15 0.24 −0.03 0.26 −6 0 0.06 0.16 0.27 0.05 0.21 −7 0 0.08 0.21 0.34−0.04 0.34 −8 0 0.07 0.22 0.36 0.05 0.26

From FIG. 12, in the case of no chromatic aberration, it is clearlyunderstandable that the presented diopter range is substantialquasi-clear visual area. Here, the quasi-clear visual area is defined asa region in which the logMAR visual acuity is 0.2 or lower.

Further, when the Abbe number is 60, it is clearly understandable thatthe diopter minus range is the quasi-clear visual area.

Further, the data of the power error and the astigmatism in Table 16 arecalculated as the power error and the astigmatism at the visual angle of60° (cycloduction angle of 30°) using the data of the lens form of Table14. It is proved from these data that the power error is equal to orlower than a diopter setting minimum unit of 0.25 [D], and theastigmatism, even though it is slightly large at +6 [D] or higher,satisfies the astigmatism of 0.5 [D] which is frequently used forspectacle lens design standards.

Specifically, for the presented diopter range (±8 [D] or less), both injudgement of the power error and the astigmatism which areconventionally the aberrations for correcting designs, and in the visualacuity function in the case that the chromatic aberration is not takeninto consideration, it has not been clear that which design of diopterpart is needed to be corrected.

However, in this example, by using this visual acuity function includingthe chromatic aberration, performance of a spectacle lens becomes clear,and corrective designing for the performance of the spectacle lensbecomes very easy.

Further, from a viewpoint of performance correction of spectacle lenses,it is proved that the quasi-clear visual area is appropriate at a visualangle of 50°.

Further, although the expression of the clear visual diameter is used inthis example, besides that, evaluation by a percentage rate of the clearvisual area on a lens surface may be used, or the clear visual angle maybe directly displayed to be evaluated.

Further, the visual acuity function may be improved in such a mannerthat the chromatic aberration is added to the above-describedconventional art, “Measurement of visual acuity: a critical review, A.M. A. Arch. Ophthal” (45(6): 704-725, 1951), or to the one disclosed inJapanese Examined Patent Application No. Sho 42-9416 (or an improvedone). In such cases, for example, the following visual acuity functioncan be derived.visual acuity function=log₁₀[1+2.8×(sphere error+L×cylerror)]+β×chromatic aberration of magnification   (c)

where, L is a coefficient within a range of 0.5≦L≦0.8, and when atangential error is denoted by T and a saggital error is denoted by S,the sphere error and the cyl error are expressed by the followingequations (d) and (e) respectively:sphere error=min (|T|, |S|)   (d)cyl error=∥T|−|S∥  (e)

INDUSTRIAL AVAILABILITY

According to the present invention, evaluation of an optical system withrespect to visual acuity can be appropriately performed, with chromaticaberration of magnification of the optical system being taken intoconsideration. Furthermore, according to the present invention, anoptical system can be appropriately designed while the chromaticaberration of magnification of the optical system is taken intoconsideration.

1. A performance evaluation method of an optical system, comprising:evaluating a performance of the optical system based on a combination ofa first deterioration amount and a second deterioration amount, a totaldeterioration amount of a visual acuity which is due to aberrations inthe optical system, the total deterioration amount being a sum of thefirst and second deterioration amounts when the visual acuity isexpressed as a logarithmic visual acuity, the first deterioration amountbeing only due to an aberration other than a chromatic aberration ofmagnification and the second deterioration amount being only due to thechromatic aberration of magnification.
 2. The performance evaluationmethod of the optical system according to claim 1, wherein theperformance of the optical system is evaluated using a visual acuityfunction that defines a value of the visual acuity based on the totaldeterioration amount by combining a first term for obtaining the firstdeterioration amount and a second term for obtaining the seconddeterioration amount.
 3. The performance evaluation method of theoptical system according to claim 2, wherein the visual acuity functionincludes a sum of the first term and the second term when the visualacuity is expressed by the logarithmic visual acuity.
 4. The performanceevaluation method of the optical system according to claim 3, whereinthe second term includes a product of a parameter which expresses avalue of the chromatic aberration of magnification and a predeterminedproportional constant.
 5. The performance evaluation method of theoptical system according to claim 4, wherein the second term covers arange of the chromatic aberration of magnification in which the smallfield tritanopia phenomenon occurs.
 6. The performance evaluation methodof the optical system according to claim 3, wherein the first termincludes a parameter which has a first value for a far region in apredetermined direction and a second value for a near region which iscloser to an eyeball side than the far region in the direction, thefirst value and the second value being different values.
 7. Theperformance evaluation method of the optical system according to claim6, wherein the first term includes a parameter which expresses a powererror, and a parameter which expresses an astigmatism or a residualastigmatism.
 8. The performance evaluation method of the optical systemaccording to claim 6, further comprising: setting plural evaluationpoints in advance on a surface of an optical element which forms theoptical system, where a ray is capable of passing through the surface;and evaluating the performance of the optical system based on 1) a meritfunction; or 2) a function which is substantially equivalent to themerit function, the merit function being expressed as: $\begin{matrix}\begin{matrix}{{{merit}\mspace{14mu}{function}} = {{a \times {\sum\limits_{n = 1}^{m}\;( {{u_{n} \cdot {far}}\mspace{14mu}{vision}_{n}} )^{2}}} +}} \\{{\mspace{191mu}}{{b{\sum\limits_{n = 1}^{m}\;( {{v_{n} \cdot {near}}\mspace{14mu}{vision}_{n}} )^{2}}} +}} \\{\mspace{191mu}{c \times {\sum\limits_{n = 1}^{m}\;( {w_{n} \cdot {DIST}_{n}} )^{2}}}}\end{matrix} & (f)\end{matrix}$ where: m is a natural number expressing a number ofevaluation points; the far vision_(n) is a value of the visual acuityfunction at an n^(th) evaluation point when looking the far region; thenear vision_(n) is a value of the visual acuity function at the n^(th)evaluation point when looking in the near region; DIST_(n) is a value ofa distortion aberration at the n^(th) evaluation point; a, b, c arepredetermined coefficients; u_(n), v_(n), w_(n) are coefficients of then^(th) evaluation point.
 9. The performance evaluation method of theoptical system according to claim 6, further comprising: setting pluralevaluation points in advance on a surface of an optical element whichforms the optical system, where a ray being capable of passing throughthe surface; and evaluating the performance of the optical system basedon 1) a merit function, or 2) a function which is substantiallyequivalent to the merit function, the merit function being expressed as:$\begin{matrix}\begin{matrix}{{{merit}\mspace{14mu}{function}} = {{a \times {\sum\limits_{n = 1}^{m}\;( {{u_{n} \cdot {far}}\mspace{14mu}{vision}_{n}} )^{2}}} +}} \\{{\mspace{191mu}}{{b{\sum\limits_{n = 1}^{m}\;( {{v_{n} \cdot {near}}\mspace{14mu}{vision}_{n}} )^{2}}} +}} \\{\mspace{191mu}{c \times {\sum\limits_{n = 1}^{m}\;( {{w_{n} \cdot {residual}}\mspace{14mu}{DIST}_{n}} )^{2}}}}\end{matrix} & (g)\end{matrix}$ where: m is a natural number expressing a number ofevaluation points; the far vision_(n) is a value of the visual acuityfunction at an n^(th) evaluation point when looking in the far region;the near vision_(n) is a value of the visual acuity function at then^(th) evaluation point when looking in the near region; residualDIST_(n) is a value of a distortion aberration at the n^(th) evaluationpoint; a, b, c are predetermined coefficients; u_(n), v_(n), w_(n), arecoefficients of the n^(th) evaluation point.
 10. The performanceevaluation method of the optical system according to claim 3, whereinthe visual acuity function is expressed as:visual acuity function=α×[(powererror)²+(K×astigmatism)²]^(1/2)+β×chromatic aberration of magnification,where: α is a coefficient within a range of 0.25≦α≦0.65, β is acoefficient within a range of 0.2≦β≦1.2, and K is a coefficient within arange of 0.2≦K<1.
 11. The performance evaluation method of the opticalsystem according to claim 3, wherein the visual acuity function isexpressed as:visual acuity function=α×[(power error)²+(K×residualastigmatism)²]^(1/2)+β×chromatic aberration of the magnification, where:α is a coefficient within a range of 0.25≦α≦0.65, β is a coefficientwithin a range of 0.2≦β≦1.2, and K is a coefficient within a range of0.2≦K<1.
 12. The performance evaluation method of the optical systemaccording to claim 3, wherein the visual acuity function is expressedas:visual acuity function=log₁₀[1+2.8×(sphere error+L×cylerror)]+β×chromatic aberration of magnification, where: L is acoefficient within a range of 0.5≦L≦0.8, and when a tangential error isdenoted by T and a sagittal error is denoted by S:sphere error=min (|T|, |S|),cyl error=∥T|−|S∥.
 13. The performance evaluation method of the opticalsystem according to claim 1, further comprising: setting pluralevaluation points in advance on a surface of an optical element whichforms the optical system, where a ray is capable of passing through thesurface; and evaluating the performance of the optical system at each ofthe evaluation points.
 14. A designing method of an optical systemcomprising the performance evaluation method according to claim
 1. 15.The designing method according to claim 14, further comprising: changinga value of a variable parameter by predetermined steps; evaluating avisual acuity of a virtual optical element which is defined by a valueof the variable parameter and a value of a fixed parameter for each ofthe predetermined steps based on an evaluation of the performanceevaluation method of claim 1; and specifying an optimum value of thevariable parameter that corresponds to a predetermined step in which theevaluation becomes optimum.
 16. The designing method according to claim15, wherein the variable parameter includes a chromatic aberration ofmagnification of the optical system or an optical value of the opticalsystem that corresponds to the chromatic aberration of magnification.17. An optical system which is manufactured using the designing methodof the optical system according to claim 14.